A section of a composite wall with the dimensions shown below has uniform temperatures of 200°C and 50°C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA = 70 W/(m K), kB = 60 W/(m K), kc = 40 W/(m K) and kD = 20 W/(m K), determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces. including a contact resistance of 0.1 K/W at each of the interfaces.

Question

GIVEN

• Composite wall

• Thermal conductivities:

? kA = 70 W/(m K)

? kB = 60 W/(m K)

? kC = 40 W/(m K)

? kD = 20 W/(m K)

• Surface temperatures

? Left side (TAs) = 200°C

? Right side (TDs) = 50°C

• Contact resistance at each interface (Ri) = 0.1 K/W FIND

(a) Rate of heat transfer through the wall (q) (b) Temperatures at the interfaces

ASSUMPTIONS

• One dimensional conduction

• The system is in steady state

SKETCH

Answer 1

The thermal circuit for the composite wall with contact resistances is shown below



The values of the individual resistances, are.



(a) The total resistance for this system is



The total rate of heat transfer through the composite wall is given by



(b) The average temperature on the A side of the interface between material A and material B and C

(T1A) can be determined by examining the conduction through material A alone